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[null,"1.","Record Nr.",null,"UNISA996418254503316"]
[null,null,"Autore",null,"Bracci Filippo"]
[null,null,"Titolo",null,"Continuous Semigroups of Holomorphic Self-maps of the Unit Disc [[electronic resource] /] / by Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal"]
[null,null,"Pubbl/distr/stampa",null,"Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020"]
[null,null,"ISBN",null,"3-030-36782-7"]
[null,null,"Edizione",null,"[1st ed. 2020.]"]
[null,null,"Descrizione fisica",null,"1 online resource (XXVII, 566 p. 18 illus.)"]
[null,null,"Collana",null,"Springer Monographs in Mathematics, , 1439-7382"]
[null,null,"Disciplina",null,"512.2"]
[null,null,"Soggetti",null,"Functions of complex variables"]
[{"$nulls":4},"Dynamics"]
[{"$nulls":4},"Ergodic theory"]
[{"$nulls":4},"Functional analysis"]
[{"$nulls":4},"Differential equations"]
[{"$nulls":4},"Geometry"]
[{"$nulls":4},"Functions of a Complex Variable"]
[{"$nulls":4},"Dynamical Systems and Ergodic Theory"]
[{"$nulls":4},"Functional Analysis"]
[{"$nulls":4},"Ordinary Differential Equations"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,"Nota di contenuto",null,"Part I: Preliminaries -- 1 Hyperbolic geometry and interation -- 2. Holomorphic functions with non-negative real part -- 3. Univalent functions -- 4. Carathéodory’s prime ends theory -- 5. Hyperbolic geometry in simply connected domains -- 6. Quasi-geodesics and localization -- 7. Harmonic measures and Bloch functions -- Part II: Semigroups -- 8 Semigroups of holomorphic functions -- 9 Models and Koenigs functions -- 10 Inﬁnitesimal generators -- 11 Extension to the boundary -- 12 Boundary ﬁxed points and inﬁnitesimal generators -- 13 Fixed points, backward invariant sets and petals -- 14 Contact points -- 15 Poles of the inﬁnitesimal generators -- 16 Rate of convergence at the Denjoy-Wolffpoint -- 17 Slopes of orbits at the Denjoy-Wolffpoint -- 18 Topological invariants."]
[null,null,null,"Sommario/riassunto","The book faces the interplay among dynamical properties of semigroups, analytical properties of infinitesimal generators and "]
[{"$nulls":4},"geometrical properties of Koenigs functions. The book includes precise descriptions of the behavior of trajectories, backward orbits, petals and boundary behavior in general, aiming to give a rather complete picture of all interesting phenomena that occur. In order to fulfill this task, we choose to introduce a new point of view, which is mainly based on the intrinsic dynamical aspects of semigroups in relation with the hyperbolic distance and a deep use of Carathéodory prime ends topology and Gromov hyperbolicity theory. This work is intended both as a reference source for researchers interested in the subject, and as an introductory book for beginners with a (undergraduate) background in real and complex analysis. For this purpose, the book is self-contained and all non-standard (and, mostly, all standard) results are proved in details."]